Please explain books solution fully i dont understand numbers where does 387.50 come from and all....

Smith buys 1000 shares of stock at 5.00 per share and pays a commission of 2%. Six months later Smith receives a cash dividend of 20 per share, which Smith immediately reinvests commission-free in shares at a price of 4.00 per share. Six months after that Smith buys another 500 shares at a price of 4.50 per share, and pays a commission of 2%. Six months after that Smith receives another cash dividend of 0.25 per share and sells all the existing shares at 5.00 per share, again paying a 2% commission. Find the IRR for Smith's transaction in the form i⁽²⁾

SOLUTION Let time 0 represent the time of the original share purchase. Then 4 = 0 and B - 5100, the initial outlay including commission. Measuring time in 6- MEASURING THE RATE OF RETURN ON AN INVESTMENT 269 month intervals, we have t = 1 at 6 months with 4 = 200 and B = 200, since he receives and immediately reinvests the dividend of 200, buying an additional 50 shares. Then t = 2 is at 12 months with 4, = 0 and B, -2295 (buying an additional 500 shares for a total of 1550 shares), and 1-3 is at 18 months with Az = 387.50 +7595 = 7982.50 (the dividend on 1550 shares plus the proceeds from the sale of the shares after commission) and B0. The net amounts received are Co = -5100, C = 0, C--2295, and C = 7982.5, so we wish to solve the equation, -5100 - 2295-v2 + 7982.5.v2 = 0,or, equivalently, SO) = 5100(1+j)+2295(1+j) - 7982.5 = 0, where the v and factors are based on 6-month interest rates so that 12) -2;. Using a financial calculator with multiple cashflow capability such as the TI BA II PLUS or the HP-12C, the unknown interest rate is found to be j = 3.246%, or equivalently, 1(2) = 6.49%. SOLUTION Let time 0 represent the time of the original share purchase. Then 4 = 0 and B - 5100, the initial outlay including commission. Measuring time in 6- MEASURING THE RATE OF RETURN ON AN INVESTMENT 269 month intervals, we have t = 1 at 6 months with 4 = 200 and B = 200, since he receives and immediately reinvests the dividend of 200, buying an additional 50 shares. Then t = 2 is at 12 months with 4, = 0 and B, -2295 (buying an additional 500 shares for a total of 1550 shares), and 1-3 is at 18 months with Az = 387.50 +7595 = 7982.50 (the dividend on 1550 shares plus the proceeds from the sale of the shares after commission) and B0. The net amounts received are Co = -5100, C = 0, C--2295, and C = 7982.5, so we wish to solve the equation, -5100 - 2295-v2 + 7982.5.v2 = 0,or, equivalently, SO) = 5100(1+j)+2295(1+j) - 7982.5 = 0, where the v and factors are based on 6-month interest rates so that 12) -2;. Using a financial calculator with multiple cashflow capability such as the TI BA II PLUS or the HP-12C, the unknown interest rate is found to be j = 3.246%, or equivalently, 1(2) = 6.49%